Proceedings of the Annual Meeting of the Cognitive Science Society

Representations of numerical value have been assessed usingbounded (e.g., 0-1000) and unbounded (e.g., 0-?) number-linetasks, with considerable debate regarding whether one or bothtasks elicit unique cognitive strategies (e.g., addition orsubtraction) and require unique cognitive models. To test this,we examined 86 5- to 9-year-olds' addition, subtraction, andestimation skill (bounded and unbounded). Against themeasurement-skills hypothesis, estimates were even morelogarithmic on unbounded than bounded number lines andwere better described by conventional log-linear models thanby alternative cognitive models. Moreover, logarithmic indexvalues reliably predicted arithmetic scores, whereas modelparameters of alternative models failed to do so. Resultssuggest that the logarithmic-to-linear shift theory provides aunified framework for numerical estimation with highdescriptive adequacy and yields uniquely accurate predictionsfor children’s early math proficiency.